# Probability Questions

• January 2nd 2011, 05:02 PM
suchgreatheights
Probability Questions

The probability of a french hen truly having citizenship is .81, find the probability that exactly 2 hens out of three have citizenship.

and

If there is an infinite number of calling birds, and the probability of a bird actually calling is .63, find the probability of finding the first calling bird on the third attempt.

Please solve and then explain. Thanks!
• January 2nd 2011, 05:18 PM
pickslides
Quote:

Originally Posted by suchgreatheights

The probability of a french hen truly having citizenship is .81, find the probability that exactly 2 hens out of three have citizenship.

Use the binomial distribution

$\displaystyle P(2) = ^3C_2(0.81)^2\times (1-0.81)^1=\dots$
• January 2nd 2011, 05:19 PM
Chris L T521
Quote:

Originally Posted by suchgreatheights

The probability of a french hen truly having citizenship is .81, find the probability that exactly 2 hens out of three have citizenship.

Let X be the random variable that represents the number of french hens truly having citizenship. Then X has a binomial distribution with n=3 and p=.81. Now what is P(X=2)?

Quote:

If there is an infinite number of calling birds, and the probability of a bird actually calling is .63, find the probability of finding the first calling bird on the third attempt.

Please solve and then explain. Thanks!
This one is a little more interesting because you're looking for the first success after so many trials. Hence, this one is modeled by a geometric distribution where p=.63. Now what is P(X=3)?

I leave it to you to look up their corresponding pdfs and finish working out these problems. Can you proceed?
• January 2nd 2011, 05:48 PM
suchgreatheights
Well, what would be setup of the geometric distribution for the second one?
• January 2nd 2011, 08:38 PM
matheagle
P(failure on first)P(failure on second)P(success on third attempt)

=(.37)(.37)(.63)

assuming indep between these selections